It's well-known that over $\mathbb F_q$ every smooth projective conic $C$ is isomorphic to a projective line. So the formula for the motivic zeta-function $Z_{mot}(C)$ is evident since $S^n\mathbb P^1 \simeq \mathbb P^n$.

But what can one say when the finite field in the formulation of this question is replaced by an *arbitrary* field? Are there any references which can help me to determine the answer?